You should answer thus: “as Lazarus in his lifetime received evil things so will I now gladly suffer torments that future glory may be laid up for me.” For “affliction shall not rise up the second time.” Nahum 1:9

and also effectively in the legal maxim which is derived from Greek and Roman civil law

Nemo debet bis vexari pro eadem causa

No one should be called on to answer to the same complaint twice.

King Henry's motive was this, or so it is reported that he stated.

That in order to allow for the prosecution of those clerics who have been accused of committing public crimes, he wanted to bring back those practices which were in force in the courts in the time of his grandfather.
[This is questionable as many modern historians have commented that clause 3 was legally something completely new, and that no such law appertained in the time of Henry I. And if it did it was much weaker in essence.]

Henry's argument was this:

For such persons who have been caught and who have been convicted or have confessed, and have subsequently been degraded, they should thus be received for public punishment as if they were lay persons, and subject to seizure.

[Possibly reasonable, but Becket argued that this was completely contrary to the Canon Law of his time and the principle that no one should be tried for the same crime twice.]

Clause 3 was problematic. Its wording was ambiguous, perhaps deliberately so. Maitland has commented, that there were not really two trials. The first trial in the ecclesiastical court was where the cleric confessed to him crime, and as a consequence lost his place in the Church, lost his clerical status. and for this, he was defrocked, an insufficient punishment in Henry's mind for the commission of a felony, which was a kind of feudal treason. Maitland argued that Henry saw that the trial that was held in the ecclesiastical court was only a kind of preliminary hearing. The real trial of the now former cleric could now take place in the king's court, as he no longer had the Church's protection and it was in the king's court where the former cleric could receive a proper and fitting punishment for the crime he has committed. All Henry was arguing was that the Church should not protect clerics who commit felonies.But Becket insisted that the trials of clerics which take place in ecclesiastical court are full and real trials, and the punishments or penances they receive there are fit and proper. Becket argued that clerics who have committed crimes and have been thus tried, should not suffer a second trial for the same crime in another court, as this was contrary to Canon Law.But who or where do you make an appeal to for a resolution on this point of law? Becket decided that it was the Pope and his Curia who had the proper authority to make a decision on this matter. But he was formally disallowed by English customary law from communicating with and making an appeal to the Pope without the king's consent. He was also disallowed from travelling abroad. In Henry's mind it was the king who formed the highest level of appeal in England. He was sovereign in his country. He had been given full authority to administer justice in England by his coronation. He was only answerable to God for his acts, not the Pope. It was thus that the quarrel between Becket and Henry erupted into a major controversy, which took many years to reach a kind of resolution, and which involved Becket attempting to go abroad, his trial for treason, following which he escaped into exile in France, and the years of negotiation which followed. The Pope did condemn clause 3.

[William] the Conqueror was accustomed to intervene when for a serious crime the sentence of the Christian court seemed to be too lenient and to keep the defendant in jail until after a further review of the case had taken place.

R. Génestal, The Privilegium fori Volume. II, p. 100, asserts without evidence to support that the custom of France and Normandy was then in line with the procedure described in Article III of Clarendon. We think not. For Normandy at least we can get an idea of how clerical criminals were treated from a case described by Arnulf of Lisieux probably prior to 1166 This concerns a counterfeiter from Bayeux imprisoned by the king's officers, who was released through the efforts of the ordinary [bishop], and subject to leave the duchy after degradation (Patrologia Latina, Volume CCI, Letters of Arnulf of Lisieux 144 edited by F. Barlow. p. 176-177, in Simon Bishop of Meaux, quoted by Haskins, op. cit., p. 171). In our opinion, this does not mean that the cleric in question appeared in the court of the king, but that he was under the threat of such an appearance if the ordinary had claimed it in time; he seems to have benefited from a compromise negotiated by the bishop, while the justices of Henry II tried to assert justly that the case belonged in the ducal court, if not for this but for other crimes which clerics were also guilty (the penalty for counterfeiters was mutilation).

There is a certain Henry dwelling amongst you who is from the land and episcopacy of my birth. He was promoted irregularly into holy orders by a foreign bishop who happened to be there. But later on, after the passage of time, he was involved in many crimes, confessing to counterfeiting for which he was publicly convicted, of the manufacture of false coins which he had not been afraid to circulate throughout the whole city of Bayeaux, and with which evily to defraud the unwary. He was arrested, and thrown into prison by the king's most noble officers where, of course, his legs were bound with iron fetters.

At length, however, after considerable effort and labour by the bishop of the city he was delivered from this, on pain of banishment in perpetuity from the whole of the province of Normandy. And of course he was brought before the archbishop whence the circle of the tonsure around his head was broken, his priestly garments torn from him, degraded he was cast out from whole land [of Normandy] forever.